PROJECT SUMMARY Social and health scientists share a long-standing interest in trends in inequality, for example, health dispari- ties. But they have largely ignored the lagged selection bias that is prevalent in trend studies and can render comparison of the groups invalid over time. Lagged selection bias occurs when there is a secular change in the dynamics of selection into treatment and control groups. If the mechanism of selection into these groups changes over time, the simple comparison in the outcome across treatment groups will be nave because these treatment groups are not the same. Without recognizing and solving the lagged selection bias, studies may yield artefactual trends in health disparities and make misleading suggestions for public policy makers. The overall objective of this proposed project is to propose a semi-parametric approach to mitigate the lagged selection bias under the counterfactual framework, complemented with a difference-in-difference approach to further remove the universal period effects for treatment and control groups. This approach promises to change survey design in ways that will make this approach feasible for all the trend studies. More specifically, this proposal intends to reach four aims. Aim 1: Establish a counterfactual framework to create comparable treatment and control groups between two time points using propensity score matching or weighting methods. Then I will complement these methods with a difference-in-difference approach to estimate the changes in health disparities. Aim 2: Extend these methods to multiple time points to estimate the trends in health dispari- ties over a long period of time. Aim 3: Extend these methods to multiple time points and multiple-valued caus- es to estimate the trends in health disparities over a long period of time. Aim 4: Evaluate the lagged selection bias in health disparities trends studies using NCHS (National Center for Health Statistics) data (e.g., National Health Interview Survey) and suggest ways to improve the surveys in order to adequately use the methods de- veloped in this project. The endogeneity problem is one of the major threats for causal inference in observa- tional studies. Even though sufficient attention has been paid to cross-sectional designs and cohort study de- sign, not enough attention has been focused on the lagged selection bias in trend studies using pooled cross- sectional designs. This project is innovative because it develops an unprecedented method to mitigate the lagged selection bias in trend studies using pooled cross-sectional design under the ignorability assumption. This method will fill the gap in the current methodology of causal inference. This project's focus is on the trends in health disparities, but the methods developed here are readily applicable to other contexts.